Question

General Motor Company is currently paying a dividend of $1.40 per year. The dividends are expected to grow at a rate of 18% for the next three years and then a constant rate of 5% thereafter. What is the value of its current stock price? The discount rate is 10%.

Answer 1

This question requires application of dividend discount model, where the current value of stock is present value of dividends expected in future.

By dividend discount model, Value of Stock today is mathematically represented as:

Where V_n represents terminal value, which is the value of constantly growing dividends starting from year n+1.

Here, let us first define the dividends.

D₁ = $1.40 * (1+18%) = $1.65

D₂ = $1.65 * (1+18%) = $1.95

D₃ = $1.95 * (1+18%) = $2.30

D₄ = $2.30 * (1+5%) = $2.42

Terminal Value, V₃ = D₄/(r – g) = 2.42/(10% - 5%) = $48.305

V₀, Value of Share today = D₁/(1 + r)¹ + D₂/(1 + r)² + D₃/(1 + r)³ + V₃/(1 + r)³

V₀ = 1.65/(1 + 10%)¹ + 1.95/(1 + 10%)² + 2.30/(1 + 10%)³+ 48.305/(1 + 10%)³

V₀ = $41.13 - - > Value of share today